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A065170 Permutation t->t-3 of Z, folded to N. 2
7, 5, 9, 3, 11, 1, 13, 2, 15, 4, 17, 6, 19, 8, 21, 10, 23, 12, 25, 14, 27, 16, 29, 18, 31, 20, 33, 22, 35, 24, 37, 26, 39, 28, 41, 30, 43, 32, 45, 34, 47, 36, 49, 38, 51, 40, 53, 42, 55, 44, 57, 46, 59, 48, 61, 50, 63, 52, 65, 54, 67, 56, 69, 58, 71, 60, 73, 62, 75, 64, 77, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This permutation consists of just three cycles, which are infinite.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.

Index entries for sequences that are permutations of the natural numbers

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

Let f: Z -> N be given by f(z) = 2z if z>0 else 2|z|+1, with inverse g(z) = z/2 if z even else (1-z)/2. Then a(n) = f(g(n)-3).

G.f.: x*(x^8-x^7+4*x^6-4*x^5+4*x^4-4*x^3-3*x^2-2*x+7) / ((x-1)^2*(x+1)). - Colin Barker, Feb 18 2013

a(n) = -6*(-1)^n+n for n>6. a(n) = a(n-1)+a(n-2)-a(n-3) for n>9. - Colin Barker, Mar 07 2014

MATHEMATICA

CoefficientList[Series[(x^8 - x^7 + 4 x^6 - 4 x^5 + 4 x^4 - 4 x^3 - 3 x^2 - 2 x + 7)/((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 08 2014 *)

LinearRecurrence[{1, 1, -1}, {7, 5, 9, 3, 11, 1, 13, 2, 15}, 80] (* Harvey P. Dale, Oct 19 2018 *)

PROG

(PARI) Vec(x*(x^8-x^7+4*x^6-4*x^5+4*x^4-4*x^3-3*x^2-2*x+7)/((x-1)^2*(x+1))  + O(x^100)) \\ Colin Barker, Mar 07 2014

CROSSREFS

Inverse permutation to A065166.

Sequence in context: A195059 A195493 A195399 * A113816 A073823 A304136

Adjacent sequences:  A065167 A065168 A065169 * A065171 A065172 A065173

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen, Oct 19 2001

STATUS

approved

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Last modified January 17 15:16 EST 2019. Contains 319225 sequences. (Running on oeis4.)